A nonlinear dynamics perspective on some aspects of towing operations relevant to safety and energy efficiency

Scheduled and emergency towing operations are carried out daily, both at sea and in restricted waters, as a means of transporting goods, aiding ships during berthing and casting-off or rescuing units in distress. Even in mild weather conditions, such activities can pose serious threats to the safety of the personnel and units involved and to the environment. This study investigates the dynamics of a tug-tow system, where towing is carried out by means of a single elastic towing line. A simplified model is used, in which the tug is modelled as a point-particle with a prescribed motion, while the dynamics of the towed object is modelled as a 3-DOF (surge/sway/yaw) nonlinear dynamical system. Equilibria of the system are analysed through a bifurcation analysis technique, supplemented by time-domain simulations, if/when necessary. An example application is reported for the case of towing of a barge-like hull, showing the effects of several parameters: ship speed, towline length, water depth and wind. The performed calculations confirm that, depending on the configuration parameters, multiple stable/unstable steady-state towing positions may exist. It is also clarified in this study that, in the absence of stable equilibria, the potentially dangerous oscillating phenomenon called “fishtailing” takes place.